Numerical simulation of wave motions on a rotating attracting spherical zone

作者：Ostapenko V V^*; Speshilova A V; Cherevko A A; Chupakhin A P

来源：Computational Mathematics and Mathematical Physics, 2015, 55(3): 470-486.

DOI：10.1134/S0965542515030124

• conservation laws for shallow water equations on a rotating attracting spherical zone
• Riemann problem
• equilibrium
• zonal flows
• shock-capturing difference scheme
• decay of ridges in the form of chevrons and elliptic annuli

The Riemann problem for the shallow water model on a rotating attracting spherical zone numerically is solved. A shock-capturing difference scheme is constructed that approximates the system of conservation laws describing discontinuous solutions of the given model. The Riemann problem is formulated as one of developing a wave process from initial data representing a spherical zone covered by various equilibria and zonal flows. Two Riemann problems are numerically simulated: the breakdown of water "ridges" of various shapes at equilibrium and propagation of contact discontinuity perturbations between an equilibrium and a zonal flow. The general properties of such solutions independent of the geometric configuration of the domains occupied by elementary solutions in the initial data are demonstrated.

• 出版日期2015-3